Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold 6 Li in a 2D optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we develop here may be applied to measurements of other transport quantities, including the optical conductivity and thermopower. arXiv:1802.09456v2 [cond-mat.quant-gas]

Layered organic superconductors of the BEDT family are model systems for understanding the interplay of the Mott transition with superconductivity, magnetic order and frustration, ingredients that are essential to understand superconductivity also in the cuprate high-temperature superconductors. Recent experimental studies on a hole-doped version of the organic compounds reveals an enhancement of superconductivity and a rapid crossover between two different conducting phases above the superconducting dome. One of these phases is a Fermi liquid, the other not. Using plaquette cellular dynamical mean field theory with state of the art continuoustime quantum Monte Carlo calculations, we study this problem with the two-dimensional Hubbard model on the anisotropic triangular lattice. Phase diagrams as a function of temperature T and interaction strength U/t are obtained for anisotropy parameters t = 0.4t, t = 0.8t and for various fillings. As in the case of the cuprates, we find, at finite doping, a first-order transition between two normal-state phases. One of theses phases has a pseudogap while the other does not. At temperatures above the critical point of the first-order transition, there is a Widom line where crossovers occur. The maximum (optimal) superconducting critical temperature T m c at finite doping is enhanced by about 25% compared with its maximum at half-filling and the range of U/t where superconductivity appears is greatly extended. These results are in broad agreement with experiment. Also, increasing frustration (larger t /t) significantly reduces magnetic ordering, as expected. This suggests that for compounds with intermediate to high frustration, very light-doping should reveal the influence of the first-order transition and associated crossovers. These crossovers could possibly be even visible in the superconducting phase through subtle signatures. We also predict that destroying the superconducting phase by a magnetic field should reveal the first-order transition between metal and pseudogap. Finally, we predict that electron-doping should also lead to an increased range of U/t for superconductivity but with a reduced maximum Tc. This work also clearly shows that the superconducting dome in organic superconductors is tied to the Mott transition and its continuation as a transition separating pseudogap phase from correlated metal in doped compounds, as in the cuprates. Contrary to heavy fermions for example, the maximum Tc is definitely not attached to an antiferromagnetic quantum critical point. That can also be verified experimentally.

Superfluid stiffness ρs is a defining characteristic of the superconducting state, allowing phase coherence and supercurrent. It is accessible experimentally through the penetration depth. Coexistence of d-wave superconductivity with other phases in underdoped cuprates, such as antiferromagnetism (AF) or charge-density waves (CDW), may drastically alter ρs. To shed light on this physics, the zero-temperature value of ρs = ρzz along the c-axis was computed for different values of Hubbard interaction U and different sets of tight-binding parameters describing the high-temperature superconductors YBCO and NCCO. We used Cellular Dynamical Mean-Field Theory for the one-band Hubbard model with exact diagonalization as impurity solver and state-of-the-art bath parametrization. We conclude that Mott physics plays a dominant role in determining the superfluid stiffness on the hole-doped side of the phase diagram. On the electron-doped side, antiferromagnetism wins over superconductivity near half-filling. But upon approaching optimal electron-doping, homogeneous coexistence between superconductivity and antiferromagnetism causes the superfluid stiffness to drop sharply. Hence, on the electron-doped side, it is competition between antiferromagnetism and d-wave superconductivity that plays a dominant role in determining the value of ρzz near half-filling. At large overdoping, ρzz behaves in a more BCS-like manner in both the electron-and hole-doped cases. We comment on some qualitative implications of these results for the superconducting transition temperature.